RESUMO
This work presents an extension of the slash Lindley-Weibull distribution, of which it can be considered a modification. The new family is obtained by using the quotient of two independent random variables: a two-parameter Lindley-Weibull distribution divided by a power of the exponential distribution with parameter equal to 2. We present the pdf and cdf of the new distribution, analyzing their risk functions. Some statistical properties are studied and the moments and coefficients of asymmetry and kurtosis are shown. The parameter estimation problem is carried out by the maximum likelihood method. The method is assessed by a Monte Carlo simulation study. We use nutrition data, which are characterized by high kurtosis, to illustrate the usefulness of the proposed model.
RESUMO
The Birnbaum-Saunders distribution is a widely studied model with diverse applications. Its origins are in the modeling of lifetimes associated with material fatigue. By using a motivating example, we show that, even when lifetime data related to fatigue are modeled, the Birnbaum-Saunders distribution can be unsuitable to fit these data in the distribution tails. Based on the nice properties of the Birnbaum-Saunders model, in this work, we use a modified skew-normal distribution to construct such a model. This allows us to obtain flexibility in skewness and kurtosis, which is controlled by a shape parameter. We provide a mathematical characterization of this new type of Birnbaum-Saunders distribution and then its statistical characterization is derived by using the maximum-likelihood method, including the associated information matrices. In order to improve the inferential performance, we correct the bias of the corresponding estimators, which is supported by a simulation study. To conclude our investigation, we retake the motivating example based on fatigue life data to show the good agreement between the new type of Birnbaum-Saunders distribution proposed in this work and the data, reporting its potential applications.